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$Q$-divisible modules

1971
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Canadian mathematical bulletin
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1. Introduction. Let R be a ring with 1 and let Q denote the maximal left quotient ring of R [6] . In a recent paper [12] , Wei called a (left) .R-module M divisible in case Hom B (Q, 7V)#0 for each nonzero factor module N of M. Modifying the terminology slightly we call such an i?-module a Q-divisible i?-module. As shown in [12] , the class D of all Q-divisible modules is closed under factor modules, extensions, and direct sums and thus is a torsion class in the sense of Dickson [5] . It

doi:10.4153/cmb-1971-087-9
fatcat:l5mgvrfyhrcx3g65mfjlems6fy